In NHQCs, spectrum transitions usually accompany state
transitions regarding their spatial profiles [1]}, [2]}. In the NRMM,
we also discover a transition from an insulator phase
with no extended eigenstates to a mobility edge phase, in which extended
and localized eigenstates coexist. To see this, we first inspect the
inverse participation ratio (IPR), which is defined for the \(i\) th
eigenstate \(|\psi ^{i}\rangle \)  of \(H\)  in the lattice representation as
\({\rm IPR}_{i}={\textstyle \sum _{n=1}^{L}}|\psi _{n}^{i}|^{4}\) .
Here the amplitude \(\psi _{n}^{i}=\langle n|\psi ^{i}\rangle \)  and \(i=1,2,...,L\) .
In the localized phase, all eigenstates have finite IPRs. Extended
states start to appear when the minimum of IPRs, denoted as \(\min ({\rm IPR})\) ,
starts to approach zero.
